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SAN ANTONIO — It was the type of game where everyone was locked in. Even Celtics assistant coach Lawrence Frank.

He rushed up the sideline by the scorer’s table, choking the life out of his legal pad, when he spotted a play he had seen the Spurs run on film.

“Ginobili’s coming up top!’’ he yelled.

Manu Ginobili indeed curled to the top of the arc.

“Pass! Pass!’’ Frank yelled.

Tim Duncan dropped a pass to Ginobili. Frank hunched over, knowing what was going to happen next. Ginobili twisted wildly for a layup that put the Spurs up, 42-37, in the second quarter.

“That’s from I don’t even know the hours [of film],’’ said Celtics coach Doc Rivers, after his team rallied for a 107-97 win.

But all along the Boston bench, senses were heightened. The Celtics had slogged through March, slumps and skids weighing them down as they lost games to lesser teams and lost their grip on first place in the Eastern Conference.

A battle with the league’s best team was a smelling-salt game for the Celtics, who started to doze off at the wheel.

“If you don’t come in here and play, man, they’ll blow [you] out, period, point blank,’’ Garnett said. “We saw what they did to the Heat [30-point win]. We saw what they’ve been doing practically all year.’’

The Celtics didn’t have to ask if the Spurs were going to dial up the intensity to playoff levels. The fact that Duncan, Ginobili, Antonio McDyess, and Tony Parker all sat out Monday’s loss to Portland was as good a sign as any. They were resting up for a prize fight with the Celtics.

The Celtics responded with their fifth straight win at the AT&T Center.

“We knew they rested their stars and they were preparing for this game,’’ Garnett said. “We took that personal. They’re the best team in the league. If you don’t come in here and play, they’ll treat you as if you were the worst team in the league.’’

Every basket felt like a power punch. Every shot felt like a momentum shifter. Every timeout huddle felt like a turning point.

With 2:21 left in the third quarter, the Celtics had taken the lead and were trying to assume permanent control as Paul Pierce huddled with a mix of reserves.

He looked at Delonte West, Jeff Green, Von Wafer, and Jermaine O’Neal (who was making his return after missing more than two months after arthroscopic knee surgery), and told them, “We’ve got to scrap. Let’s scrap. Every loose ball. We’ve got to get to it.’’

After the Spurs controlled the glass in the first half (26-23, 8-4 offensive), the Celtics fought back in the second (20-17). After giving up 15 second-chance points in the first half, the Celtics held the Spurs to just 3 in the second. And after turning the ball over six times in the first half, the Celtics forced the Spurs to cough it up seven times.

O’Neal tipped offensive rebounds. Wafer and West ripped down rebounds. Meanwhile, the Spurs were firing cannonballs into their own ship, taking 29 3-pointers and knocking down just eight.

The Celtics, who have struggled on the road against Western Conference teams, swept the season series with the Spurs, who lost their fifth straight overall for the first time in 14 years.

It was a regular-season game with a playoff atmosphere and the Celtics treated it that way.

“There’s certain teams when you play, they have the exact same aspirations that we have,’’ Rivers said. “So when you play a team like that, you really want to play them. That’s just human nature. When we play Miami and the Lakers and Orlando and Chicago, it’s the same way.’’

Pierce, who had been slumping, flirted with a triple-double (21 points, 11 rebounds, 7 assists). Rajon Rondo had fallen into his own funk but had somewhat of a breakthrough, finishing with 22 points (11-of-20 shooting) and 14 assists.

“This is a good place to try to gather some momentum,’’ Pierce said. “You’re talking about the team with the best record and the best home record. What better place to get back on track than here?’’

If marquee matchups are the antidote, the Celtics have road games against Chicago and Miami left on the schedule, potential shocks to the system before the playoffs start.

“It was a good, intense game,’’ Rivers said. “It’s nice to have some of those in the regular season.’’